Answer:
As used in this epigram, "nomadic" is modifying the noun "longings".
Explanation:
This question is tricky because the word order in the poem is inverted. In English, the adjective is placed before the noun it modifies: beautiful girl, blue sky, bright eyes, etc. But here, the author has chosen to place the adjective "nomadic" after the noun it refers to, which would be "longings". What the epigraph means is that our old nomadic longings, that is, that desire we have to move from one place to another, which we inherited from our ancestors, will burst out if we stay in one place for too long.
The poem by John Meyers O'Hara is used as an epigraph (short quotation) at the beginning of "The Call of the Wild", a novel by Jack London.
